Now keeping these things in mind we introduce, besides the creation-annihilation operators for finite energy (physical) excitations, an infinite number of conformal primary operators of arbitrary dimension and spin, which do not carry any energy-momentum. These primaries can either be thought of as living on the celestial sphere, or, on a spherical cross-section of the null-cone in momentum space. One may be tempted to call these primaries "soft operators" [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, but let us emphasise that at this stage we cannot identify them with the soft operators which appear in the soft-theorems. In fact, this identification is one of the problems that we try to solve in this paper. In any case, for simplicity of notation we will refer to these primaries as soft-operators but with the caveat, that they are not necessarily the same as the ones appearing in the soft theorems.
